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<p>In this paper, we analyze the long-time dynamics of small solutions to the 1<i>d</i> cubic nonlinear Schrödinger equation (NLS) with a trapping potential. We show that every small solution decomposes into a small solitary wave and a radiation term exhibiting modified scattering. Our analysis also establishes the long-time behavior of solutions to perturbations of the integrable cubic NLS in the presence of solitons.</p>

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Long-Time Dynamics of Small Solutions to 1d Cubic Nonlinear Schrödinger Equations with A Trapping Potential

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  • 出版模式：

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  • 发表日期：

    2026年5月2日

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  • Gong Chen

摘要

In this paper, we analyze the long-time dynamics of small solutions to the 1d cubic nonlinear Schrödinger equation (NLS) with a trapping potential. We show that every small solution decomposes into a small solitary wave and a radiation term exhibiting modified scattering. Our analysis also establishes the long-time behavior of solutions to perturbations of the integrable cubic NLS in the presence of solitons.